Gold ring with emerald, engraved initials, lost near Capitol Street

I lost my gold ring yesterday around 3pm outside the Jackson Public Library on Capitol Street. It's a 14k yellow gold signet-style ring, size 6, with a small emerald set in the bezel and a faint hairline scratch along the band. Inside the band, the initials 'S.A.' are engraved, and the ring has sentimental value—it's a family heirloom from my grandmother. I’m really hoping someone picked it up and kept it safe near the fountain area; it means a lot to me and I’d be incredibly grateful to get it back.